Does this suffer from the same issue?
It isn't necessarily an important issue. Maybe nobody will figure out they can take down your service that way. Maybe rate limiting is enough. Maybe you can solve it by having servers dedicated to hashing.
I was just curious about the performance characteristics:
Suppose that three people have passwords that are each randomly chosen and 6 characters long. A typical laptop can crack those passwords in about 1 hour. If you take the same passwords and protect them with PolyPasswordHasher, every computer on the planet working together cannot crack the password in 1 hour. In fact, to search the key space, it would take every computer on the planet longer than the universe is estimated to have existed.
The contradiction is that if users can log in to your service quickly, then they can try a lot of passwords quickly. So is this more expensive than scrypt?
If an attacker has read-only disk access, they can swipe any unencrypted data. Scrypt protects you from this, and it's straightforward about the requirements and computation costs.
In practice, what kind of CPU usage would a PolyPasswordHasher scheme need?